What is the projection of $<0,8,5>$ onto $<1,2,-4>$ ?

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Answer 1 · 2016-04-26T21:19:12

$-4/sqrt(21)$

The projection of a vector $A$ along a direction $theta$ with itself is given as $|A|costheta$

Lets say here $A = <0,8,5>$
And $B = <1,2,-4>$

Their dot product is $|A| |B| costheta = 0+16-20 =-4$

So the projection is $(|A||B|costheta)/(|B|) = (-4)/sqrt(1^2+2^2+4^2) = -4/sqrt(21)$

What is the projection of <0,8,5> <0,8,5> onto <1,2,-4><1,2,-4>?